换热器优化中均分原则的适用性分析

Applicability analyses of equipartition principles in heat exchanger optimization

在许多物理过程的优化设计中,其优化结果反映为某些物理量或者函数的均匀分布,即相应的均分原则.针对两股流和三股流换热器的优化分析,讨论了热力学力场均匀性原则、ΔT/T场均匀性原则和温差场均匀性原则三项均分原则的适用性.研究表明,当换热量给定时,前两项原则既不能给出最小的换热器熵产率,又不能给出最高的换热器效能;而当换热器实现最佳传热性能时,前两项原则得不到满足.对于温差场均匀性原则,不论冷热流体间的传热系数是否为常数,均可基于理论对其进行数学证明.当冷热流体温差场完全均匀时,换热器的耗散热阻达到最小值.可见,温差场均匀性原则可以给出换热器的最佳传热性能.进一步,本文给出了简单的案例,直观地验证了上述结论.理论与案例分析的结果进一步表明,热力学力场均匀性原则和ΔT/T场均匀性原则都是基于熵产的概念得到的,而熵产从做功能力损失的角度衡量不可逆性,导致这两项原则与传热优化的目的不一致,而且其推导过程中所采用的传热定律也不符合实际的传热过程;而用于证明温差场均匀性原则的(火积)耗散则从传热能力损失的角度衡量传热过程的不可逆性,其优化目标与传热优化目标则是一致的.这就是前两项原则不适用于换热器优化分析而温差场均匀性原则适用的根本原因.

The uniform distribution of certain physical quantities or functions, referred to as the corresponding equipartition principles, can be reflected in the optimization design of many physical processes. In this paper, three equipartition principles for the optimization of two-and three-stream heat exchangers are discussed, including the uniformity principle of thermodynamic force field, uniformity principle of the field of ΔT/T, and uniformity principle of temperature difference field. The main problems are highlighted for the first two principles. It is demonstrated that for a fixed heat transfer rate, the two principles cannot lead to the minimum entropy-generation rate or the highest heat exchanger effectiveness, and they cannot be satisfied when the best heat transfer performance is achieved. For the last principle, whether the heat transfer coefficient between cold and hot fluids is constant or not, it can be directly proved using the entransy theory, and theoretical derivation shows that for a fixed ratio of heat capacity flow rates and the number of heat transfer units, a larger uniformity factor of temperature difference field gives larger heat exchanger effectiveness. It is also demonstrated that when the temperature difference field is completely uniform, the entransy-dissipation-based thermal resistance has the minimum value. Therefore, the last principle can give the optimal heat transfer performance for heat exchangers. Some simple numerical examples for the application of the three principles are also presented, and the results directly verify the theoretical analyses.Theoretical analyses and simple examples show that the uniformity principles of the thermodynamic force field and the field of ΔT/T are obtained based on the entropy-generation concept and the uniformity principle of temperature difference field is derived with the entransy dissipation concept. The former concept describes the irreversibility of heat transfer from the viewpoint of the ability to do work, and the latter concept measures irreversibility from the viewpoint of heat transfer ability. This is why the first two principles are not consistent with heat transfer optimization, whereas the last principle is. Additionally, the heat transfer law does not conform to the actual heat transfer processes in the derivation of the first principle. Therefore, the first two principles are unsuitable for heat exchanger optimization, whereas the third principle is suitable;the statement that the uniformity principle of the temperature difference field is a duplicate of the uniformity principle of the field of ΔT/T for balanced counter-flow heat exchangers is unscientific and incorrect.